On the Existence of (v,3×3,λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9

作     者：苏仁旺 王金华 SU Ren-wang1, WANG Jin-hua2(1. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;2. School of Science, Nantong University, Nantong 226007, China )

作者机构：College of Statistics and MathematicsZhejiang Gongshang University School of ScienceNantong University 

出 版 物：《Journal of Shanghai Jiaotong university(Science)》 (上海交通大学学报（英文版）)

年 卷 期：2008年第13卷第4期

页      面：482-486页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：the National Natural Science Foundation of China (No. 10771193) the Starter Foundation for the Doctors of Zhejiang Gongshang University(No. 1020XJ030517) the Natural Science Foundationof Universities of Jiangsu Province (No. 07KJB110090) the Starter Foundation for the Doctors of Nantong University (No. 07B12) 

主　　题：Splitting balanced incomplete block design group-divisible design (GDD) 

摘      要：Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.